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Math Grade 9-12 Answer Key

Polynomial Operations

Adding, subtracting, and multiplying polynomials

Answer Key
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Polynomial Operations

Adding, subtracting, and multiplying polynomials

Math - Grade 9-12

Instructions: Read each problem carefully. Simplify each expression completely and show your work.
  1. 1

    Simplify: (3x^2 + 5x - 7) + (2x^2 - 4x + 9)

    Combine like terms by matching the x^2 terms, x terms, and constants.

    The simplified expression is 5x^2 + x + 2.
  2. 2

    Simplify: (6a^2 - 3a + 8) - (2a^2 + 5a - 1)

    The simplified expression is 4a^2 - 8a + 9.
  3. 3

    Simplify: 4y(2y^2 - 3y + 5)

    Distribute 4y to each term inside the parentheses.

    The simplified expression is 8y^3 - 12y^2 + 20y.
  4. 4

    Simplify: (x + 7)(x + 3)

    The simplified expression is x^2 + 10x + 21.
  5. 5

    Simplify: (2m - 5)(m + 4)

    Use distribution or the FOIL method to multiply each pair of terms.

    The simplified expression is 2m^2 + 3m - 20.
  6. 6

    Simplify: (5p^2 + 2p - 6) + (3p^2 - 7p + 4)

    The simplified expression is 8p^2 - 5p - 2.
  7. 7

    Simplify: (7x^3 - 2x^2 + x - 9) - (3x^3 + 4x^2 - 5x + 1)

    Change the signs in the second polynomial before combining like terms.

    The simplified expression is 4x^3 - 6x^2 + 6x - 10.
  8. 8

    Simplify: -3z^2(2z - 5) + 4z

    The simplified expression is -6z^3 + 15z^2 + 4z.
  9. 9

    Simplify: (n - 6)^2

    Expand the square by multiplying (n - 6)(n - 6).

    The simplified expression is n^2 - 12n + 36.
  10. 10

    Simplify: (3x + 2)(x - 5)

    The simplified expression is 3x^2 - 13x - 10.
  11. 11

    Simplify: (4r^2 - r + 6) + (2r^2 + 9r - 11) - (r^2 + 3r + 1)

    First combine the first two polynomials, then subtract the third.

    The simplified expression is 5r^2 + 5r - 6.
  12. 12

    Simplify: 2t^2(3t^2 - 4t + 7)

    The simplified expression is 6t^4 - 8t^3 + 14t^2.
  13. 13

    Simplify: (x^2 + 4x + 1) - (2x^2 - x + 8)

    Be careful to distribute the subtraction sign to every term in the second polynomial.

    The simplified expression is -x^2 + 5x - 7.
  14. 14

    Simplify: (2b - 3)(2b + 3)

    The simplified expression is 4b^2 - 9.
  15. 15

    Simplify: (x + 2)(x^2 - 3x + 4)

    Distribute each term in the binomial across the trinomial, then combine like terms.

    The simplified expression is x^3 - x^2 - 2x + 8.
LivePhysics.com Math - Grade 9-12 - Answer Key